16  Unit 4: Earth-Sun Dynamics 5E

What factors have contributed to climate change in the past and are they contributing to climate change now?

HS-ESS2-4 Time: 5 Days

17 Investigative Phenomenon

17.1 🔬 Phenomenon

The amount of radiation received at 65°N has gone up and down over the last 750,000 years and repeats a pattern about every 100,000 years.

17.1.1 Driving Questions:

• How do we know that natural cycles aren’t causing climate change today?
• How has the Earth’s position with respect to the Sun changed over time?
• How does the Earth’s changing position with respect to the Sun affect temperatures on Earth?

18 Engage: Solar Radiation Patterns

18.1 Solar Radiation at 65°N

Connecting to our earlier questions about how Earth’s temperature has varied in the past, let’s analyze the total amount of energy from solar radiation reaching Earth at 65°N over the last 750,000 years.

Plot = require("@observablehq/plot")

// Extended Radiation Data (750k years)
radiationData = [
  {kya: 740, radiation: 460}, {kya: 720, radiation: 490},
  {kya: 700, radiation: 470}, {kya: 680, radiation: 440},
  {kya: 660, radiation: 500}, {kya: 640, radiation: 470},
  {kya: 620, radiation: 450}, {kya: 600, radiation: 480},
  {kya: 580, radiation: 510}, {kya: 560, radiation: 470},
  {kya: 540, radiation: 450}, {kya: 520, radiation: 490},
  {kya: 500, radiation: 460}, {kya: 480, radiation: 520},
  {kya: 460, radiation: 530}, {kya: 440, radiation: 480},
  {kya: 420, radiation: 460}, {kya: 400, radiation: 460}, 
  {kya: 380, radiation: 490}, {kya: 360, radiation: 470}, 
  {kya: 340, radiation: 440}, {kya: 320, radiation: 500}, 
  {kya: 300, radiation: 470}, {kya: 280, radiation: 450}, 
  {kya: 260, radiation: 480}, {kya: 240, radiation: 510}, 
  {kya: 220, radiation: 470}, {kya: 200, radiation: 450}, 
  {kya: 180, radiation: 490}, {kya: 160, radiation: 460}, 
  {kya: 140, radiation: 520}, {kya: 120, radiation: 530}, 
  {kya: 100, radiation: 480}, {kya: 80, radiation: 460}, 
  {kya: 60, radiation: 440}, {kya: 40, radiation: 470}, 
  {kya: 20, radiation: 450}, {kya: 0, radiation: 480}
]

// Vostok ice core data (kept for reference/comparison later)
iceCoreTempData = [
  {kya: 400, temp: -8}, {kya: 380, temp: -4}, {kya: 360, temp: -6},
  {kya: 340, temp: -8}, {kya: 320, temp: -3}, {kya: 300, temp: -6},
  {kya: 280, temp: -8}, {kya: 260, temp: -4}, {kya: 240, temp: -2},
  {kya: 220, temp: -6}, {kya: 200, temp: -8}, {kya: 180, temp: -4},
  {kya: 160, temp: -6}, {kya: 140, temp: -1}, {kya: 120, temp: 2},
  {kya: 100, temp: -4}, {kya: 80, temp: -6}, {kya: 60, temp: -8},
  {kya: 40, temp: -6}, {kya: 20, temp: -8}, {kya: 10, temp: -2},
  {kya: 0, temp: 0}
]

viewof timeRange = Inputs.range([0, 750], {
  step: 50,
  value: 750,
  label: "View last ___ thousand years:"
})

filteredRadData = radiationData.filter(d => d.kya <= timeRange)

Plot.plot({
  title: "Summer Radiation at 65°N Over the Past " + timeRange + ",000 Years",
  subtitle: "Solar Radiation (Watts/m²)",
  width: 750,
  height: 400,
  x: {label: "Thousands of Years Ago (kya)", reverse: true},
  y: {label: "Radiation (W/m²)", domain: [420, 550]},
  marks: [
    Plot.ruleY([480], {stroke: "#999", strokeDasharray: "4,4"}),
    Plot.areaY(filteredRadData, {x: "kya", y: "radiation", y2: 480, fill: d => d.radiation > 480 ? "#e74c3c" : "#3498db", fillOpacity: 0.4}),
    Plot.line(filteredRadData, {x: "kya", y: "radiation", stroke: "#2c3e50", strokeWidth: 2}),
    Plot.dot(filteredRadData.filter(d => d.radiation > 520), {x: "kya", y: "radiation", fill: "red", r: 5}),
    Plot.text(filteredRadData.filter(d => d.radiation > 520), {x: "kya", y: "radiation", text: d => "Peak", dy: -10, fontSize: 10})
  ]
})

18.1.1 ✅ Initial Observations

1. What pattern do you notice in the radiation data over the last 750,000 years?
2. Approximately how often does the radiation intensity peak?
3. How might this repeating pattern relate to the temperature cycles we’ve discussed previously?

19 Explore: Earth’s Orbital Cycles

19.1 The Three Orbital Cycles

How does Earth’s position affect the amount of radiation reaching Earth’s surface? Students use models of Earth’s eccentricity, tilt, and direction of tilt cycles to collect empirical evidence in order to determine whether there is a causal relationship between orbital cycles and the amount of solar radiation reaching Earth at 65° N over the last 750,000 years.

Serbian scientist Milutin Milankovitch proposed that variations in Earth’s orbit cause long-term climate cycles. Let’s explore each one.

19.1.1 Cycle 1: Eccentricity (~100,000 year cycle)

Earth’s orbit changes shape from nearly circular to more elliptical.

viewof eccentricity = Inputs.range([0, 0.06], {
  step: 0.005,
  value: 0.017,
  label: "Eccentricity (current = 0.017):"
})

// Draw orbit with variable eccentricity
{
  const width = 500;
  const height = 400;
  const cx = width / 2;
  const cy = height / 2;
  const a = 180; // semi-major axis
  const b = a * Math.sqrt(1 - eccentricity * eccentricity); // semi-minor axis
  const c = a * eccentricity; // focal distance
  
  const svg = d3.create("svg")
    .attr("width", width)
    .attr("height", height);
  
  // Draw orbit ellipse
  svg.append("ellipse")
    .attr("cx", cx + c)
    .attr("cy", cy)
    .attr("rx", a)
    .attr("ry", b)
    .attr("fill", "none")
    .attr("stroke", "#3498db")
    .attr("stroke-width", 2);
  
  // Draw Sun at one focus
  svg.append("circle")
    .attr("cx", cx)
    .attr("cy", cy)
    .attr("r", 20)
    .attr("fill", "#f1c40f");
  
  svg.append("text")
    .attr("x", cx)
    .attr("y", cy + 5)
    .attr("text-anchor", "middle")
    .attr("font-size", "12px")
    .text("☀️");
  
  // Draw Earth positions
  svg.append("circle")
    .attr("cx", cx + c + a)
    .attr("cy", cy)
    .attr("r", 10)
    .attr("fill", "#3498db");
  
  svg.append("text")
    .attr("x", cx + c + a)
    .attr("y", cy - 20)
    .attr("text-anchor", "middle")
    .attr("font-size", "10px")
    .text("Aphelion (farthest)");
  
  svg.append("circle")
    .attr("cx", cx + c - a)
    .attr("cy", cy)
    .attr("r", 10)
    .attr("fill", "#2ecc71");
  
  svg.append("text")
    .attr("x", cx + c - a)
    .attr("y", cy - 20)
    .attr("text-anchor", "middle")
    .attr("font-size", "10px")
    .text("Perihelion (closest)");
  
  // Info box
  svg.append("rect")
    .attr("x", 10)
    .attr("y", 10)
    .attr("width", 200)
    .attr("height", 80)
    .attr("fill", "#f5f5f5")
    .attr("rx", 5);
  
  svg.append("text")
    .attr("x", 20)
    .attr("y", 35)
    .attr("font-size", "12px")
    .text(`Eccentricity: ${eccentricity.toFixed(3)}`);
  
  const distDiff = ((2 * a * eccentricity) / a * 100).toFixed(1);
  svg.append("text")
    .attr("x", 20)
    .attr("y", 55)
    .attr("font-size", "12px")
    .text(`Distance variation: ${distDiff}%`);
  
  svg.append("text")
    .attr("x", 20)
    .attr("y", 75)
    .attr("font-size", "11px")
    .attr("fill", "#666")
    .text(`Cycle: ~100,000 years`);
  
  return svg.node();
}

19.1.2 Cycle 2: Obliquity (Axial Tilt) (~41,000 year cycle)

Earth’s axial tilt varies between 22.1° and 24.5°.

viewof tiltAngle = Inputs.range([22.1, 24.5], {
  step: 0.1,
  value: 23.5,
  label: "Axial Tilt (current = 23.5°):"
})

{
  const width = 500;
  const height = 350;
  
  const svg = d3.create("svg")
    .attr("width", width)
    .attr("height", height);
  
  // Draw orbital plane
  svg.append("line")
    .attr("x1", 50)
    .attr("y1", height/2)
    .attr("x2", width - 50)
    .attr("y2", height/2)
    .attr("stroke", "#ccc")
    .attr("stroke-width", 2)
    .attr("stroke-dasharray", "5,5");
  
  svg.append("text")
    .attr("x", width - 100)
    .attr("y", height/2 + 20)
    .attr("font-size", "11px")
    .attr("fill", "#999")
    .text("Orbital Plane");
  
  // Draw Earth
  const earthX = width / 2;
  const earthY = height / 2;
  const earthR = 60;
  
  svg.append("circle")
    .attr("cx", earthX)
    .attr("cy", earthY)
    .attr("r", earthR)
    .attr("fill", "#3498db");
  
  // Draw tilted axis
  const tiltRad = tiltAngle * Math.PI / 180;
  const axisLength = 120;
  
  svg.append("line")
    .attr("x1", earthX - axisLength * Math.sin(tiltRad))
    .attr("y1", earthY + axisLength * Math.cos(tiltRad))
    .attr("x2", earthX + axisLength * Math.sin(tiltRad))
    .attr("y2", earthY - axisLength * Math.cos(tiltRad))
    .attr("stroke", "#e74c3c")
    .attr("stroke-width", 3);
  
  // Angle indicator
  svg.append("text")
    .attr("x", earthX + 70)
    .attr("y", earthY - 80)
    .attr("font-size", "14px")
    .attr("font-weight", "bold")
    .attr("fill", "#e74c3c")
    .text(`${tiltAngle.toFixed(1)}°`);
  
  // Effect description
  const effect = tiltAngle > 23.5 ? "MORE extreme seasons" : tiltAngle < 23.5 ? "LESS extreme seasons" : "Current tilt";
  svg.append("rect")
    .attr("x", 20)
    .attr("y", 20)
    .attr("width", 180)
    .attr("height", 60)
    .attr("fill", "#f5f5f5")
    .attr("rx", 5);
  
  svg.append("text")
    .attr("x", 30)
    .attr("y", 45)
    .attr("font-size", "12px")
    .text(`Tilt: ${tiltAngle.toFixed(1)}°`);
  
  svg.append("text")
    .attr("x", 30)
    .attr("y", 65)
    .attr("font-size", "11px")
    .attr("fill", "#666")
    .text(effect);
  
  return svg.node();
}

19.1.3 Cycle 3: Precession (~23,000 year cycle)

Earth’s axis wobbles like a spinning top, changing which hemisphere is tilted toward the Sun at perihelion.

viewof precessionAngle = Inputs.range([0, 360], {
  step: 15,
  value: 0,
  label: "Precession angle (degrees):"
})

{
  const width = 450;
  const height = 350;
  
  const svg = d3.create("svg")
    .attr("width", width)
    .attr("height", height);
  
  const cx = width / 2;
  const cy = height / 2;
  
  // Wobble circle (path of North Pole)
  svg.append("ellipse")
    .attr("cx", cx)
    .attr("cy", cy - 80)
    .attr("rx", 50)
    .attr("ry", 20)
    .attr("fill", "none")
    .attr("stroke", "#9b59b6")
    .attr("stroke-width", 2)
    .attr("stroke-dasharray", "5,5");
  
  // Earth
  svg.append("circle")
    .attr("cx", cx)
    .attr("cy", cy)
    .attr("r", 50)
    .attr("fill", "#3498db");
  
  // Wobbling axis
  const precRad = precessionAngle * Math.PI / 180;
  const wobbleX = 30 * Math.cos(precRad);
  const wobbleY = 15 * Math.sin(precRad);
  
  svg.append("line")
    .attr("x1", cx - wobbleX)
    .attr("y1", cy + 100 - wobbleY)
    .attr("x2", cx + wobbleX)
    .attr("y2", cy - 100 + wobbleY)
    .attr("stroke", "#e74c3c")
    .attr("stroke-width", 3);
  
  // North marker
  svg.append("circle")
    .attr("cx", cx + wobbleX)
    .attr("cy", cy - 100 + wobbleY)
    .attr("r", 8)
    .attr("fill", "#e74c3c");
  
  svg.append("text")
    .attr("x", cx + wobbleX + 15)
    .attr("y", cy - 100 + wobbleY)
    .attr("font-size", "12px")
    .text("N");
  
  // Info
  svg.append("rect")
    .attr("x", 10)
    .attr("y", height - 70)
    .attr("width", 200)
    .attr("height", 60)
    .attr("fill", "#f5f5f5")
    .attr("rx", 5);
  
  svg.append("text")
    .attr("x", 20)
    .attr("y", height - 45)
    .attr("font-size", "12px")
    .text(`Precession: ${precessionAngle}°`);
  
  svg.append("text")
    .attr("x", 20)
    .attr("y", height - 25)
    .attr("font-size", "11px")
    .attr("fill", "#666")
    .text("Cycle: ~23,000 years");
  
  return svg.node();
}

19.2 🔬 Lab Activity: Milankovitch Cycle Investigation

19.2.1 Materials Needed:

• Graph paper or spreadsheet
• Colored pencils
• Calculator

19.2.2 Procedure:

Part 1: Analyzing the Cycles

1. Use the interactive simulations above to explore each cycle
2. Record observations in your data table:

Cycle	Period	Current Value	Range	Climate Effect
Eccentricity	~100,000 yrs	0.017	0.0 - 0.06	Changes total radiation received
Obliquity	~41,000 yrs	23.5°	22.1° - 24.5°	Changes seasonal contrast
Precession	~23,000 yrs	N/A	360° rotation	Changes timing of seasons

Part 2: Analyzing the Data

Review the Radiation Graph from the Engage section.

1. Which orbital cycle (Eccentricity, Obliquity, or Precession) has a period that most closely matches the major 100,000-year pattern in the radiation data?
2. How might the other two cycles affect the smaller “wiggles” in the data?

Part 3: Making a Claim

Based on your observations of the orbital models and the radiation data: 1. Construct a claim about whether Earth’s orbital cycles cause the variations in solar radiation reaching Earth. 2. Support your claim with evidence from the models and the graph.

20 Explain: Connecting Orbit to Climate

Did changes in Earth’s position cause the patterns of radiation reaching Earth’s surface and glacial-interglacial cycles?

20.1 🌍 The Mechanism

Key Insight: It’s not total yearly radiation that matters most—it’s summer radiation at high northern latitudes (around 65°N).

20.1.1 Why 65°N Matters:

1. Most of Earth’s land mass is in the Northern Hemisphere
2. Ice sheets grow when summer is NOT warm enough to melt winter snow
3. When summer radiation at 65°N is LOW, ice sheets expand
4. When summer radiation at 65°N is HIGH, ice sheets retreat

20.1.2 The Feedback Loop:

Low summer radiation → Snow persists → Ice sheets grow → 
Higher albedo → More cooling → More ice growth

20.2 Comparing Radiation and Temperature

combinedData = iceCoreTempData.map(d => {
  const rad = radiationData.find(r => r.kya === d.kya);
  return {
    kya: d.kya,
    temp: d.temp,
    radiation: rad ? rad.radiation : 480
  };
})

Plot.plot({
  title: "Temperature vs. Summer Radiation at 65°N",
  width: 750,
  height: 400,
  x: {label: "Thousands of Years Ago", reverse: true},
  y: {label: "Temperature Anomaly (°C)", axis: "left"},
  marks: [
    Plot.line(combinedData, {x: "kya", y: "temp", stroke: "#e74c3c", strokeWidth: 2}),
    Plot.dot(combinedData.filter(d => d.temp > -2), {x: "kya", y: "temp", fill: "#e74c3c", r: 6}),
    Plot.text([{x: 350, y: 2}], {x: "x", y: "y", text: d => "Temperature", fill: "#e74c3c", fontSize: 12}),
    
    // Add radiation trend for comparison (scaled to fit)
    Plot.line(combinedData, {x: "kya", y: d => (d.radiation - 480) / 10 - 6, stroke: "#3498db", strokeWidth: 1, strokeDasharray: "4,2"}),
    Plot.text([{x: 350, y: -5}], {x: "x", y: "y", text: d => "Radiation (scaled)", fill: "#3498db", fontSize: 10})
  ]
})

20.2.1 💡 Key Ideas: Earth-Sun Dynamics

1. Temperatures on Earth have fluctuated greatly during human history, marked by glacial and interglacial periods
2. A pattern exists in the frequency of these fluctuations (~100,000 years)
3. The pattern is explained by cyclical changes in Earth’s orbit shape and tilt
4. These changes cause ice sheets to expand and retreat
5. Current orbital parameters suggest Earth should be cooling, yet global temperatures are increasing

21 Elaborate: Solar Activity vs. Glacial Cycles

How well does activity from the Sun correlate with glacial-interglacial cycles?

21.1 Solar Radiation Data

Some claim changes in the Sun’s output (Solar Activity) are causing climate changes. We know orbital cycles cause the Ice Ages, but what about the Sun itself? And what about the warming we see today?

Let’s examine the evidence for the Sun’s role in recent history:

solarData = [
  {year: 1880, tsi: 1365.5, temp: -0.16},
  {year: 1900, tsi: 1365.7, temp: -0.08},
  {year: 1920, tsi: 1365.6, temp: -0.25},
  {year: 1940, tsi: 1365.8, temp: 0.12},
  {year: 1960, tsi: 1365.9, temp: -0.01},
  {year: 1980, tsi: 1366.1, temp: 0.26},
  {year: 2000, tsi: 1366.0, temp: 0.42},
  {year: 2020, tsi: 1361.0, temp: 1.02}
]

Plot.plot({
  title: "Solar Output (TSI) vs Global Temperature",
  width: 700,
  height: 400,
  x: {label: "Year"},
  marks: [
    Plot.line(solarData, {x: "year", y: d => (d.tsi - 1360) * 2, stroke: "#f1c40f", strokeWidth: 2}),
    Plot.line(solarData, {x: "year", y: d => d.temp * 3 + 5, stroke: "#e74c3c", strokeWidth: 2}),
    Plot.text([{x: 1900, y: 12}], {x: "x", y: "y", text: d => "Solar Output", fill: "#f1c40f", fontSize: 12}),
    Plot.text([{x: 1900, y: 7}], {x: "x", y: "y", text: d => "Temperature", fill: "#e74c3c", fontSize: 12})
  ]
})

21.1.1 ✅ Analysis Questions

1. Has solar output increased significantly since 1980?
2. Has temperature increased significantly since 1980?
3. Can changes in solar output explain recent warming? Why or why not?

22 Evaluate: Are Orbital Factors Causing Warming Today?

How do we know that orbital factors are not causing climate change today?

22.1 📊 Putting It Together

Based on current orbital parameters:

Parameter	Current Value	Trend	Climate Effect
Eccentricity	0.017	Decreasing	Less seasonal variation
Obliquity	23.44°	Decreasing	Less extreme seasons
Precession	NH summer at aphelion	Changing slowly	Cooler NH summers

Conclusion: Based on Milankovitch cycles alone, Earth should be gradually cooling. The fact that Earth is warming despite this indicates another factor is at play.

This sets up our next investigation: What IS causing the warming?

---

22.2 📝 Earth-Sun Dynamics Quiz

Question 1: What is the approximate period of the eccentricity cycle? - A) 23,000 years - B) 41,000 years - C) 100,000 years - D) 1 million years

Question 2: Why is summer radiation at 65°N latitude so important for ice ages? - A) It’s where most people live - B) It’s where most land mass is located, and ice sheets need cool summers to persist - C) The Sun is closest to Earth at this latitude - D) Ocean currents are strongest here

Question 3: Earth’s current axial tilt is approximately: - A) 22.1° - B) 23.5° - C) 24.5° - D) 45°

Question 4: According to Milankovitch cycles, what should Earth’s climate be doing right now? - A) Warming rapidly - B) Staying constant - C) Cooling gradually - D) Experiencing an ice age

Question 5: What causes the ~100,000 year glacial-interglacial cycle? - A) Changes in the Sun’s energy output - B) Volcanic activity - C) Changes in Earth’s orbital eccentricity - D) Human activity

Question 6: The precession cycle affects climate by: - A) Changing total solar radiation received - B) Changing which season occurs at perihelion vs aphelion - C) Changing Earth’s distance from the Sun - D) Changing the Sun’s output

Question 7: If Earth’s axial tilt increased to 24.5°, seasons would become: - A) Less extreme - B) More extreme - C) Unchanged - D) Reversed

Question 8: What is the significance of global warming occurring despite Milankovitch cycles predicting cooling? - A) Milankovitch cycles are wrong - B) Another factor must be causing the warming - C) The Sun’s output has increased dramatically - D) Earth’s orbit has changed unexpectedly

Answers: 1-C, 2-B, 3-B, 4-C, 5-C, 6-B, 7-B, 8-B